Rockfish Historical Harvest Estimates

Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
   
3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

• Model: LB_fit_5pH

• Model Run: HR_fitLBR_2bias_hierPcomp_5pH_infPr_thru2023_1e+06_7kn_2025-01-22 (Naming convention: modelname_thruYEAR_iters_rundate)

• Proportion of parmaters converged (Rhat <= 1.1): 0.9356

• See end of document for summary of unconverged parameters.

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

• Model development notes:
  • NA

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

And black rockfish releases…

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

Figure 8.- Residuals from logbook harvests

SWHS residuals

Figure 9.- Residuals from SWHS harvests.

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

Figure 11.- Mean percent of harvest by charter anglers.

When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.

parameter n badRhat_avg beta3_pH 8 5.677035 beta0_pH 10 2.034856 beta3_black 1 1.712481 beta2_pH 11 1.698637 beta0_black 2 1.542205 beta1_black 12 1.511333 beta1_pH 22 1.504607 beta1_yellow 3 1.338583 beta3_yellow 2 1.327958 mu_beta0_pH 1 1.281240

parameter n badRhat_avg beta2_yellow 7 1.272123 tau_beta0_pH 3 1.260369 tau_beta0_yellow 1 1.242417 beta2_black 5 1.194757 beta2_pelagic 1 1.190766 beta1_pelagic 4 1.189850 beta0_yellow 4 1.177827 beta4_pelagic 2 1.161320 tau_beta0_pelagic 2 1.155882 beta0_pelagic 3 1.123104

Table 2. Summary of unconverged parameters by area

	afognak	BSAI	CI	CSEO	eastside	EWYKT	NG	northeast	NSEI	NSEO	PWSI	PWSO	SOKO2SAP	SSEI	SSEO	WKMA
beta0_black	0	0	1	0	0	0	0	0	0	0	0	1	0	0	0	0
beta0_pelagic	0	0	1	0	0	0	1	0	0	0	0	0	1	0	0	0
beta0_pH	0	0	0	1	0	0	0	0	1	1	0	0	0	0	1	1
beta0_yellow	0	0	0	0	0	0	1	0	0	1	0	1	0	0	0	1
beta1_black	1	0	1	0	1	0	1	1	0	1	1	1	1	1	1	1
beta1_pelagic	1	0	1	0	0	0	1	0	0	0	0	0	0	0	0	1
beta1_pH	1	1	0	1	1	1	1	1	1	1	0	1	1	1	1	1
beta1_yellow	0	1	0	0	0	0	1	0	0	0	0	0	0	0	0	1
beta2_black	0	0	1	1	0	1	1	0	0	0	0	1	0	0	0	0
beta2_pelagic	0	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0
beta2_pH	1	1	0	1	0	0	0	1	1	1	0	0	0	0	1	1
beta2_yellow	0	0	0	1	0	1	0	0	1	1	0	0	0	1	1	1
beta3_black	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0
beta3_pH	0	0	0	1	0	0	0	0	1	1	0	0	0	0	1	1
beta3_yellow	0	0	0	1	0	0	0	0	0	1	0	0	0	0	0	0
beta4_pelagic	0	0	0	0	1	0	0	0	0	0	0	0	1	0	0	0
mu_beta0_pH	0	0	0	0	0	0	0	0	0	0	1	0	0	0	0	0
tau_beta0_pelagic	0	0	1	0	0	0	1	0	0	0	0	0	0	0	0	0
tau_beta0_pH	0	0	0	0	0	0	1	0	0	0	1	0	0	0	0	0
tau_beta0_yellow	0	0	1	0	0	0	0	0	0	0	0	0	0	0	0	0

Parameter estimates:

Summary Table of Parameter Estimates

Parameter	mean	sd	Lower_CI	Median	Upper_CI
mu_bc_H[1]	-0.133	0.070	-0.263	-0.135	0.014
mu_bc_H[2]	-0.099	0.046	-0.177	-0.103	0.006
mu_bc_H[3]	-0.434	0.071	-0.567	-0.434	-0.292
mu_bc_H[4]	-0.981	0.195	-1.369	-0.975	-0.607
mu_bc_H[5]	0.901	0.960	-0.156	0.708	3.385
mu_bc_H[6]	-2.214	0.325	-2.827	-2.215	-1.566
mu_bc_H[7]	-0.478	0.114	-0.716	-0.474	-0.263
mu_bc_H[8]	0.237	0.348	-0.361	0.204	1.065
mu_bc_H[9]	-0.302	0.131	-0.556	-0.300	-0.041
mu_bc_H[10]	-0.118	0.067	-0.243	-0.120	0.019
mu_bc_H[11]	-0.104	0.040	-0.176	-0.105	-0.023
mu_bc_H[12]	-0.244	0.105	-0.467	-0.240	-0.048
mu_bc_H[13]	-0.120	0.081	-0.277	-0.121	0.039
mu_bc_H[14]	-0.281	0.094	-0.461	-0.281	-0.099
mu_bc_H[15]	-0.340	0.055	-0.448	-0.341	-0.231
mu_bc_H[16]	-0.339	0.381	-1.000	-0.372	0.512
mu_bc_R[1]	1.348	0.145	1.066	1.345	1.634
mu_bc_R[2]	1.489	0.090	1.308	1.493	1.660
mu_bc_R[3]	1.420	0.136	1.151	1.421	1.684
mu_bc_R[4]	0.990	0.192	0.594	1.003	1.342
mu_bc_R[5]	1.141	0.461	0.249	1.130	2.031
mu_bc_R[6]	-1.554	0.429	-2.420	-1.545	-0.769
mu_bc_R[7]	0.286	0.189	-0.085	0.293	0.652
mu_bc_R[8]	0.543	0.203	0.132	0.546	0.931
mu_bc_R[9]	0.383	0.198	-0.043	0.399	0.737
mu_bc_R[10]	1.337	0.123	1.083	1.341	1.564
mu_bc_R[11]	1.142	0.076	0.996	1.142	1.293
mu_bc_R[12]	0.951	0.206	0.549	0.957	1.358
mu_bc_R[13]	1.045	0.101	0.845	1.044	1.258
mu_bc_R[14]	0.989	0.142	0.705	0.989	1.266
mu_bc_R[15]	0.869	0.097	0.674	0.870	1.055
mu_bc_R[16]	1.219	0.116	1.007	1.215	1.461
tau_pH[1]	2.852	0.281	2.331	2.838	3.428
tau_pH[2]	2.854	0.338	2.240	2.837	3.558
tau_pH[3]	2.874	0.430	2.114	2.841	3.788
tau_pH[4]	6.618	1.201	4.496	6.525	9.236
beta0_pH[1,1]	0.548	0.208	0.116	0.551	0.939
beta0_pH[2,1]	1.312	0.229	0.857	1.316	1.752
beta0_pH[3,1]	1.382	0.249	0.856	1.391	1.838
beta0_pH[4,1]	1.653	0.272	1.081	1.661	2.156
beta0_pH[5,1]	-0.486	0.433	-1.244	-0.518	0.655
beta0_pH[6,1]	0.167	0.632	-1.207	0.246	1.068
beta0_pH[7,1]	0.416	0.524	-0.759	0.656	1.008
beta0_pH[8,1]	-0.521	0.295	-1.197	-0.505	-0.031
beta0_pH[9,1]	-0.481	0.367	-1.216	-0.434	0.037
beta0_pH[10,1]	0.295	0.236	-0.172	0.296	0.750
beta0_pH[11,1]	0.127	0.615	-0.668	-0.046	1.797
beta0_pH[12,1]	0.625	0.229	0.178	0.630	1.065
beta0_pH[13,1]	0.214	0.436	-0.614	0.185	1.108
beta0_pH[14,1]	-0.292	0.495	-1.022	-0.364	1.175
beta0_pH[15,1]	0.621	0.521	-0.408	0.627	1.637
beta0_pH[16,1]	2.100	0.313	1.342	2.131	2.623
beta0_pH[1,2]	2.608	0.241	2.106	2.635	3.007
beta0_pH[2,2]	2.880	0.212	2.379	2.907	3.229
beta0_pH[3,2]	2.393	0.280	1.840	2.405	2.906
beta0_pH[4,2]	2.532	0.330	1.740	2.619	2.988
beta0_pH[5,2]	4.358	1.468	2.032	4.157	7.781
beta0_pH[6,2]	2.802	0.301	2.229	2.817	3.299
beta0_pH[7,2]	1.889	0.190	1.491	1.906	2.218
beta0_pH[8,2]	2.776	0.267	2.274	2.806	3.124
beta0_pH[9,2]	2.713	0.641	1.431	2.757	3.653
beta0_pH[10,2]	3.657	0.232	3.078	3.680	4.045
beta0_pH[11,2]	-4.908	0.277	-5.458	-4.907	-4.373
beta0_pH[12,2]	-4.872	0.461	-5.869	-4.839	-4.089
beta0_pH[13,2]	-4.652	0.412	-5.497	-4.634	-3.878
beta0_pH[14,2]	-5.623	0.458	-6.508	-5.620	-4.774
beta0_pH[15,2]	-4.083	0.300	-4.671	-4.083	-3.488
beta0_pH[16,2]	-4.859	0.368	-5.599	-4.847	-4.172
beta0_pH[1,3]	1.307	0.281	0.708	1.328	1.761
beta0_pH[2,3]	1.929	0.352	1.096	2.015	2.433
beta0_pH[3,3]	2.078	0.412	1.210	2.123	2.705
beta0_pH[4,3]	2.435	0.565	1.159	2.631	3.135
beta0_pH[5,3]	1.225	2.489	-4.039	1.211	6.495
beta0_pH[6,3]	-1.073	1.514	-2.571	-1.546	3.204
beta0_pH[7,3]	-2.139	0.793	-3.820	-2.106	-0.697
beta0_pH[8,3]	0.289	0.179	-0.061	0.294	0.640
beta0_pH[9,3]	-0.053	0.330	-0.695	-0.053	0.594
beta0_pH[10,3]	0.777	0.329	0.020	0.803	1.300
beta0_pH[11,4]	-0.505	0.584	-1.755	-0.443	0.520
beta0_pH[12,4]	-0.856	0.686	-2.145	-0.852	0.390
beta0_pH[13,4]	-1.269	0.936	-2.927	-1.143	0.418
beta0_pH[14,4]	-0.562	0.848	-2.140	-0.614	2.152
beta0_pH[15,4]	-0.349	0.299	-0.823	-0.386	0.340
beta0_pH[16,4]	-0.563	0.476	-1.509	-0.568	0.629
beta0_pH[11,5]	-0.811	0.219	-1.263	-0.797	-0.413
beta0_pH[12,5]	-2.107	0.423	-2.744	-2.179	-1.034
beta0_pH[13,5]	-0.422	0.655	-1.792	-0.215	0.521
beta0_pH[14,5]	-0.954	0.206	-1.357	-0.955	-0.553
beta0_pH[15,5]	-1.146	0.161	-1.459	-1.151	-0.823
beta0_pH[16,5]	-1.121	0.844	-3.404	-0.778	-0.371
beta1_pH[1,1]	3.081	0.373	2.415	3.062	3.884
beta1_pH[2,1]	2.457	0.391	1.792	2.421	3.346
beta1_pH[3,1]	2.594	0.491	1.791	2.521	3.692
beta1_pH[4,1]	3.013	0.566	2.179	2.924	4.363
beta1_pH[5,1]	2.016	0.493	1.033	2.000	3.049
beta1_pH[6,1]	2.585	0.956	1.356	2.370	5.155
beta1_pH[7,1]	2.116	1.227	0.456	2.000	4.827
beta1_pH[8,1]	3.261	0.909	2.069	3.054	5.754
beta1_pH[9,1]	2.113	0.512	1.430	2.046	3.224
beta1_pH[10,1]	2.295	0.331	1.661	2.281	2.978
beta1_pH[11,1]	6.640	1.316	4.448	6.387	10.086
beta1_pH[12,1]	2.741	0.286	2.184	2.744	3.299
beta1_pH[13,1]	5.497	1.212	3.609	5.323	8.518
beta1_pH[14,1]	15.184	4.838	8.694	14.088	27.446
beta1_pH[15,1]	7.482	1.851	4.417	7.331	11.241
beta1_pH[16,1]	12.117	3.976	6.602	11.603	20.552
beta1_pH[1,2]	2.263	5.351	0.008	0.996	17.895
beta1_pH[2,2]	3.109	9.354	0.007	1.090	16.769
beta1_pH[3,2]	1.270	0.383	0.649	1.257	1.895
beta1_pH[4,2]	3.974	13.002	0.012	0.951	31.993
beta1_pH[5,2]	9.761	30.305	0.000	0.737	110.063
beta1_pH[6,2]	8.600	34.150	0.000	1.222	121.760
beta1_pH[7,2]	2.954	10.164	0.000	0.285	26.573
beta1_pH[8,2]	1.376	4.329	0.000	0.172	15.705
beta1_pH[9,2]	1.556	6.732	0.000	1.075	3.233
beta1_pH[10,2]	82.576	121.805	0.000	3.440	360.651
beta1_pH[11,2]	6.821	0.313	6.195	6.818	7.432
beta1_pH[12,2]	6.786	0.611	5.791	6.704	8.130
beta1_pH[13,2]	7.144	0.452	6.316	7.126	8.089
beta1_pH[14,2]	7.522	0.483	6.628	7.516	8.511
beta1_pH[15,2]	6.618	0.314	6.001	6.618	7.223
beta1_pH[16,2]	7.585	0.391	6.857	7.571	8.359
beta1_pH[1,3]	1.960	0.484	1.181	1.919	2.921
beta1_pH[2,3]	0.808	2.968	0.001	0.465	2.643
beta1_pH[3,3]	0.636	0.598	0.001	0.583	1.716
beta1_pH[4,3]	0.844	1.711	0.001	0.526	2.908
beta1_pH[5,3]	4.567	4.959	1.369	3.111	17.096
beta1_pH[6,3]	4.173	5.692	1.410	3.045	14.049
beta1_pH[7,3]	2.985	0.785	1.573	2.941	4.677
beta1_pH[8,3]	2.741	0.316	2.144	2.736	3.386
beta1_pH[9,3]	2.160	0.379	1.405	2.166	2.874
beta1_pH[10,3]	2.615	0.398	1.967	2.579	3.462
beta1_pH[11,4]	3.368	0.998	2.265	3.229	6.212
beta1_pH[12,4]	3.803	0.688	2.566	3.786	5.115
beta1_pH[13,4]	3.796	1.103	2.390	3.404	5.960
beta1_pH[14,4]	3.165	1.620	1.303	3.011	4.943
beta1_pH[15,4]	2.937	0.613	2.117	2.895	3.976
beta1_pH[16,4]	5.211	4.910	2.465	3.167	20.853
beta1_pH[11,5]	2.826	1.341	1.064	2.721	5.616
beta1_pH[12,5]	5.016	3.985	2.473	3.904	15.349
beta1_pH[13,5]	4.457	2.444	2.379	3.752	11.763
beta1_pH[14,5]	4.214	4.430	1.796	3.228	13.740
beta1_pH[15,5]	3.299	1.808	1.878	2.925	7.737
beta1_pH[16,5]	2.923	1.536	0.530	2.957	5.710
beta2_pH[1,1]	0.497	0.172	0.269	0.468	0.911
beta2_pH[2,1]	0.497	0.330	0.183	0.429	1.239
beta2_pH[3,1]	0.449	0.310	0.170	0.385	1.053
beta2_pH[4,1]	0.398	0.189	0.179	0.367	0.806
beta2_pH[5,1]	1.321	1.582	0.112	0.691	5.609
beta2_pH[6,1]	0.845	1.387	0.104	0.347	5.120
beta2_pH[7,1]	-0.570	1.526	-4.764	-0.018	1.296
beta2_pH[8,1]	0.413	0.447	0.154	0.312	1.367
beta2_pH[9,1]	0.713	0.790	0.166	0.504	3.021
beta2_pH[10,1]	0.806	0.772	0.271	0.602	2.737
beta2_pH[11,1]	0.232	0.064	0.125	0.226	0.376
beta2_pH[12,1]	1.194	0.582	0.533	1.056	2.656
beta2_pH[13,1]	0.277	0.082	0.163	0.264	0.472
beta2_pH[14,1]	0.258	0.056	0.177	0.248	0.397
beta2_pH[15,1]	0.237	0.081	0.137	0.221	0.419
beta2_pH[16,1]	0.693	0.382	0.311	0.618	1.479
beta2_pH[1,2]	-0.994	4.111	-9.534	-0.321	6.442
beta2_pH[2,2]	-3.635	3.206	-10.927	-3.231	1.180
beta2_pH[3,2]	-3.832	2.625	-10.284	-3.274	-0.582
beta2_pH[4,2]	-3.700	2.937	-10.594	-3.234	0.875
beta2_pH[5,2]	-2.371	3.918	-10.187	-2.436	5.362
beta2_pH[6,2]	-3.418	3.285	-10.488	-3.193	3.281
beta2_pH[7,2]	-3.248	3.511	-10.590	-3.225	4.433
beta2_pH[8,2]	-2.943	3.795	-10.613	-2.942	4.931
beta2_pH[9,2]	-3.517	3.376	-10.796	-3.251	3.877
beta2_pH[10,2]	-3.973	3.391	-11.082	-3.777	3.198
beta2_pH[11,2]	-6.882	2.413	-12.650	-6.438	-3.480
beta2_pH[12,2]	-2.899	2.502	-9.258	-1.856	-0.543
beta2_pH[13,2]	-3.529	2.172	-9.355	-2.797	-1.318
beta2_pH[14,2]	-4.692	2.286	-10.681	-4.165	-1.794
beta2_pH[15,2]	-6.547	2.396	-12.626	-6.062	-3.292
beta2_pH[16,2]	-7.073	2.564	-13.588	-6.475	-3.613
beta2_pH[1,3]	3.655	2.462	0.363	3.218	9.384
beta2_pH[2,3]	2.452	3.654	-5.502	2.342	9.872
beta2_pH[3,3]	1.801	3.825	-5.737	2.040	9.212
beta2_pH[4,3]	2.322	3.712	-5.744	2.291	9.664
beta2_pH[5,3]	5.221	2.910	0.346	4.967	11.622
beta2_pH[6,3]	5.392	2.845	0.670	5.161	11.852
beta2_pH[7,3]	5.266	2.862	0.866	4.903	11.906
beta2_pH[8,3]	6.547	2.654	2.324	6.181	12.587
beta2_pH[9,3]	5.452	2.690	1.414	5.087	11.690
beta2_pH[10,3]	4.987	2.852	0.584	4.731	11.430
beta2_pH[11,4]	-1.732	4.045	-10.337	-1.662	5.600
beta2_pH[12,4]	-2.286	1.996	-7.875	-1.459	-0.605
beta2_pH[13,4]	-2.148	3.621	-10.995	-1.347	2.863
beta2_pH[14,4]	-1.798	3.740	-9.581	-1.533	8.259
beta2_pH[15,4]	1.669	1.197	0.588	1.305	5.120
beta2_pH[16,4]	1.896	2.174	-0.536	1.007	7.479
beta2_pH[11,5]	-2.431	2.046	-8.242	-1.743	-0.421
beta2_pH[12,5]	-3.874	2.629	-10.318	-3.302	-0.625
beta2_pH[13,5]	-2.202	3.650	-10.179	-2.411	4.383
beta2_pH[14,5]	-4.219	2.489	-10.340	-3.638	-1.008
beta2_pH[15,5]	-4.427	2.310	-10.487	-3.875	-1.552
beta2_pH[16,5]	-2.180	4.093	-11.972	-1.646	4.249
beta3_pH[1,1]	35.734	1.075	33.712	35.701	38.054
beta3_pH[2,1]	34.314	1.926	31.336	34.061	39.058
beta3_pH[3,1]	35.794	1.879	32.693	35.561	40.034
beta3_pH[4,1]	36.084	1.915	32.757	35.892	40.313
beta3_pH[5,1]	29.298	3.201	25.135	28.262	36.722
beta3_pH[6,1]	40.565	3.350	32.862	41.574	45.240
beta3_pH[7,1]	30.136	10.010	18.480	25.673	45.724
beta3_pH[8,1]	38.979	2.252	34.677	38.910	44.414
beta3_pH[9,1]	31.107	2.101	27.268	31.099	35.570
beta3_pH[10,1]	32.790	1.139	30.738	32.739	35.139
beta3_pH[11,1]	36.900	2.572	33.351	36.333	43.446
beta3_pH[12,1]	30.546	0.530	29.464	30.557	31.570
beta3_pH[13,1]	39.203	2.254	35.391	38.930	44.562
beta3_pH[14,1]	41.603	2.071	37.973	41.397	45.608
beta3_pH[15,1]	41.694	2.469	36.958	41.769	45.781
beta3_pH[16,1]	44.825	0.742	43.263	44.908	45.925
beta3_pH[1,2]	33.086	8.835	18.662	34.743	44.509
beta3_pH[2,2]	29.386	6.074	18.853	28.855	42.549
beta3_pH[3,2]	41.707	1.653	39.741	41.831	43.772
beta3_pH[4,2]	31.992	9.451	18.556	29.248	45.218
beta3_pH[5,2]	30.291	8.089	18.483	29.523	45.126
beta3_pH[6,2]	33.212	5.831	19.190	35.082	43.783
beta3_pH[7,2]	29.067	7.431	18.437	27.949	44.629
beta3_pH[8,2]	28.763	7.415	18.392	27.507	44.247
beta3_pH[9,2]	38.511	8.883	19.033	43.754	45.783
beta3_pH[10,2]	29.493	5.540	19.209	29.143	42.117
beta3_pH[11,2]	43.363	0.143	43.135	43.346	43.679
beta3_pH[12,2]	43.138	0.253	42.553	43.148	43.607
beta3_pH[13,2]	43.841	0.143	43.532	43.856	44.099
beta3_pH[14,2]	43.309	0.151	43.077	43.290	43.652
beta3_pH[15,2]	43.384	0.149	43.144	43.367	43.707
beta3_pH[16,2]	43.489	0.157	43.200	43.487	43.787
beta3_pH[1,3]	39.984	0.858	37.999	40.058	41.238
beta3_pH[2,3]	32.057	7.329	18.615	33.141	44.966
beta3_pH[3,3]	32.389	7.021	18.890	32.499	44.691
beta3_pH[4,3]	27.600	6.932	18.304	26.647	43.443
beta3_pH[5,3]	27.030	6.234	18.402	26.609	41.656
beta3_pH[6,3]	30.670	4.209	20.241	31.853	38.414
beta3_pH[7,3]	25.345	1.789	22.801	24.865	29.294
beta3_pH[8,3]	41.503	0.215	41.109	41.511	41.900
beta3_pH[9,3]	33.750	0.436	32.956	33.777	34.607
beta3_pH[10,3]	36.053	0.550	34.476	36.104	36.865
beta3_pH[11,4]	39.466	7.056	29.076	43.620	45.887
beta3_pH[12,4]	42.135	0.563	41.051	42.153	42.952
beta3_pH[13,4]	39.034	5.914	29.836	42.811	44.634
beta3_pH[14,4]	40.867	4.652	29.275	42.202	45.660
beta3_pH[15,4]	29.949	0.415	29.184	29.933	30.833
beta3_pH[16,4]	30.939	3.546	29.075	29.640	43.061
beta3_pH[11,5]	40.122	0.876	38.469	40.131	41.664
beta3_pH[12,5]	38.672	1.776	36.111	38.460	42.802
beta3_pH[13,5]	38.189	3.947	31.054	40.698	41.660
beta3_pH[14,5]	39.980	0.940	38.587	39.745	42.506
beta3_pH[15,5]	40.672	0.286	40.038	40.702	41.160
beta3_pH[16,5]	37.961	4.480	29.187	39.185	45.732
beta0_pelagic[1]	1.951	0.513	0.572	2.114	2.423
beta0_pelagic[2]	1.427	0.288	0.472	1.483	1.781
beta0_pelagic[3]	0.257	0.366	-0.700	0.315	0.845
beta0_pelagic[4]	0.307	0.318	-0.378	0.312	0.953
beta0_pelagic[5]	0.649	1.352	-2.856	1.282	1.686
beta0_pelagic[6]	1.547	0.239	0.948	1.582	1.847
beta0_pelagic[7]	1.494	0.207	1.037	1.513	1.770
beta0_pelagic[8]	1.853	0.153	1.548	1.863	2.124
beta0_pelagic[9]	2.066	0.706	0.621	2.204	2.856
beta0_pelagic[10]	2.511	0.245	1.764	2.556	2.817
beta0_pelagic[11]	0.681	0.127	0.445	0.677	0.934
beta0_pelagic[12]	1.762	0.137	1.495	1.760	2.030
beta0_pelagic[13]	0.588	0.145	0.309	0.586	0.859
beta0_pelagic[14]	0.413	0.183	0.051	0.416	0.757
beta0_pelagic[15]	-0.223	0.123	-0.458	-0.225	0.031
beta0_pelagic[16]	0.543	0.127	0.294	0.546	0.787
beta1_pelagic[1]	0.302	0.522	0.000	0.061	1.751
beta1_pelagic[2]	0.168	0.284	0.000	0.037	1.138
beta1_pelagic[3]	0.875	0.614	0.001	0.743	2.554
beta1_pelagic[4]	0.895	0.350	0.206	0.881	1.665
beta1_pelagic[5]	0.795	1.460	0.000	0.004	4.456
beta1_pelagic[6]	0.105	0.313	0.000	0.001	0.919
beta1_pelagic[7]	0.319	1.267	0.000	0.001	5.738
beta1_pelagic[8]	0.118	0.492	0.000	0.001	0.971
beta1_pelagic[9]	0.764	0.818	0.000	0.710	2.413
beta1_pelagic[10]	0.096	0.261	0.000	0.002	0.900
beta1_pelagic[11]	2.375	0.253	1.895	2.373	2.908
beta1_pelagic[12]	2.627	0.264	2.131	2.622	3.153
beta1_pelagic[13]	2.238	0.424	1.512	2.188	3.212
beta1_pelagic[14]	3.173	0.696	2.126	3.034	4.762
beta1_pelagic[15]	2.519	0.233	2.074	2.517	2.987
beta1_pelagic[16]	2.989	0.262	2.480	2.985	3.513
beta2_pelagic[1]	2.285	3.249	-4.304	1.971	9.682
beta2_pelagic[2]	2.297	3.199	-4.295	1.875	9.383
beta2_pelagic[3]	2.469	2.638	0.063	1.711	9.242
beta2_pelagic[4]	2.835	2.474	0.144	2.109	9.165
beta2_pelagic[5]	0.017	4.080	-8.098	-0.057	8.493
beta2_pelagic[6]	1.016	4.017	-7.740	1.208	8.584
beta2_pelagic[7]	0.955	3.915	-8.600	1.397	8.641
beta2_pelagic[8]	0.334	4.096	-8.683	0.399	8.299
beta2_pelagic[9]	1.708	3.566	-6.675	1.528	8.932
beta2_pelagic[10]	0.867	4.168	-7.985	0.998	8.779
beta2_pelagic[11]	3.919	2.429	1.028	3.255	10.583
beta2_pelagic[12]	6.113	2.735	2.086	5.708	12.699
beta2_pelagic[13]	1.843	2.106	0.335	0.975	7.966
beta2_pelagic[14]	0.615	0.752	0.227	0.458	1.866
beta2_pelagic[15]	5.763	2.364	2.257	5.479	11.896
beta2_pelagic[16]	5.523	2.747	1.232	5.145	12.025
beta3_pelagic[1]	27.827	7.761	18.412	24.981	44.774
beta3_pelagic[2]	30.707	8.498	18.548	29.622	45.367
beta3_pelagic[3]	30.332	5.050	22.137	30.038	43.048
beta3_pelagic[4]	25.524	2.886	21.528	25.330	32.382
beta3_pelagic[5]	33.760	9.654	18.566	33.529	45.987
beta3_pelagic[6]	30.038	7.831	18.468	28.973	44.719
beta3_pelagic[7]	29.399	8.220	18.410	27.953	44.985
beta3_pelagic[8]	29.113	7.707	18.476	27.717	44.642
beta3_pelagic[9]	28.995	6.161	18.842	27.172	43.271
beta3_pelagic[10]	29.119	8.027	18.318	27.850	44.859
beta3_pelagic[11]	43.175	0.338	42.380	43.190	43.785
beta3_pelagic[12]	43.459	0.229	43.060	43.451	43.897
beta3_pelagic[13]	42.764	0.918	40.781	42.859	44.503
beta3_pelagic[14]	43.048	1.252	40.350	43.096	45.440
beta3_pelagic[15]	43.257	0.203	42.880	43.246	43.669
beta3_pelagic[16]	43.265	0.234	42.690	43.262	43.706
mu_beta0_pelagic[1]	0.913	0.853	-0.838	0.958	2.516
mu_beta0_pelagic[2]	1.668	0.580	0.132	1.764	2.571
mu_beta0_pelagic[3]	0.617	0.409	-0.202	0.619	1.427
tau_beta0_pelagic[1]	1.207	2.391	0.065	0.661	5.529
tau_beta0_pelagic[2]	3.456	5.989	0.107	1.895	18.114
tau_beta0_pelagic[3]	1.933	1.454	0.220	1.560	5.644
beta0_yellow[1]	-0.543	0.207	-1.050	-0.518	-0.226
beta0_yellow[2]	0.458	0.225	-0.265	0.489	0.763
beta0_yellow[3]	-0.315	0.197	-0.743	-0.303	0.030
beta0_yellow[4]	0.797	0.325	-0.167	0.864	1.193
beta0_yellow[5]	-1.243	0.423	-2.081	-1.241	-0.398
beta0_yellow[6]	0.245	0.210	-0.162	0.247	0.646
beta0_yellow[7]	0.994	0.356	-0.242	1.047	1.349
beta0_yellow[8]	0.785	0.561	-0.962	0.955	1.291
beta0_yellow[9]	-0.028	0.311	-0.586	-0.040	0.562
beta0_yellow[10]	0.238	0.149	-0.055	0.237	0.534
beta0_yellow[11]	-1.718	0.547	-2.694	-1.759	-0.232
beta0_yellow[12]	-3.557	0.430	-4.477	-3.535	-2.779
beta0_yellow[13]	-3.531	0.497	-4.686	-3.476	-2.683
beta0_yellow[14]	-1.808	0.705	-2.879	-1.945	-0.108
beta0_yellow[15]	-2.767	0.408	-3.602	-2.751	-2.012
beta0_yellow[16]	-2.313	0.436	-3.210	-2.285	-1.534
beta1_yellow[1]	0.478	0.610	0.000	0.330	1.715
beta1_yellow[2]	1.168	0.541	0.620	1.044	3.138
beta1_yellow[3]	0.681	0.359	0.102	0.649	1.402
beta1_yellow[4]	1.436	0.814	0.641	1.201	3.850
beta1_yellow[5]	3.387	3.752	1.280	2.943	7.993
beta1_yellow[6]	2.301	0.356	1.621	2.299	2.994
beta1_yellow[7]	15.712	19.715	1.278	5.700	66.691
beta1_yellow[8]	2.810	4.493	0.005	1.688	15.447
beta1_yellow[9]	1.515	0.618	0.699	1.470	2.504
beta1_yellow[10]	2.667	0.496	1.798	2.631	3.708
beta1_yellow[11]	1.931	0.532	0.891	1.940	2.906
beta1_yellow[12]	2.343	0.439	1.561	2.321	3.304
beta1_yellow[13]	2.711	0.499	1.897	2.642	3.924
beta1_yellow[14]	1.998	0.623	0.651	2.034	3.082
beta1_yellow[15]	2.054	0.407	1.292	2.034	2.906
beta1_yellow[16]	2.130	0.441	1.339	2.111	3.032
beta2_yellow[1]	-2.848	2.884	-9.185	-2.432	2.074
beta2_yellow[2]	-3.068	2.616	-9.584	-2.444	-0.091
beta2_yellow[3]	-3.084	2.508	-9.012	-2.482	-0.127
beta2_yellow[4]	-2.733	2.707	-9.544	-1.936	-0.089
beta2_yellow[5]	-4.286	2.946	-11.487	-3.717	-0.506
beta2_yellow[6]	3.553	2.137	0.960	3.031	8.873
beta2_yellow[7]	-4.172	2.913	-10.761	-3.699	2.408
beta2_yellow[8]	-2.166	4.047	-10.690	-1.992	6.529
beta2_yellow[9]	3.729	2.714	0.161	3.367	9.805
beta2_yellow[10]	-4.822	2.739	-11.301	-4.318	-0.946
beta2_yellow[11]	-3.732	2.420	-10.067	-3.084	-0.810
beta2_yellow[12]	-3.985	2.320	-10.237	-3.357	-1.323
beta2_yellow[13]	-3.918	2.160	-9.813	-3.343	-1.344
beta2_yellow[14]	-4.143	2.990	-11.425	-3.240	-0.229
beta2_yellow[15]	-3.735	2.282	-10.040	-3.126	-1.151
beta2_yellow[16]	-4.167	2.427	-10.440	-3.465	-1.294
beta3_yellow[1]	28.257	7.681	18.370	26.547	44.797
beta3_yellow[2]	29.013	2.144	23.564	28.885	33.104
beta3_yellow[3]	32.897	3.103	24.933	32.932	39.024
beta3_yellow[4]	29.229	3.463	22.294	28.154	35.870
beta3_yellow[5]	33.281	1.747	29.290	33.423	36.081
beta3_yellow[6]	39.649	0.520	38.718	39.614	40.828
beta3_yellow[7]	20.251	2.248	18.414	19.946	27.021
beta3_yellow[8]	26.553	6.063	18.451	25.904	43.293
beta3_yellow[9]	37.656	2.537	35.452	37.604	42.935
beta3_yellow[10]	29.356	0.460	28.258	29.411	30.005
beta3_yellow[11]	44.648	3.017	31.290	45.362	45.971
beta3_yellow[12]	43.381	0.457	42.512	43.343	44.331
beta3_yellow[13]	44.775	0.420	43.888	44.845	45.480
beta3_yellow[14]	42.842	4.084	29.348	44.095	45.770
beta3_yellow[15]	45.288	0.497	44.233	45.332	45.977
beta3_yellow[16]	44.613	0.643	43.421	44.602	45.836
mu_beta0_yellow[1]	0.093	0.562	-1.065	0.093	1.271
mu_beta0_yellow[2]	0.139	0.495	-0.906	0.164	1.119
mu_beta0_yellow[3]	-2.280	0.661	-3.258	-2.392	-0.516
tau_beta0_yellow[1]	2.329	4.964	0.099	1.168	10.591
tau_beta0_yellow[2]	1.312	1.201	0.143	0.961	4.383
tau_beta0_yellow[3]	1.424	1.841	0.090	0.880	5.778
beta0_black[1]	0.101	0.192	-0.300	0.125	0.438
beta0_black[2]	1.906	0.132	1.665	1.909	2.154
beta0_black[3]	1.308	0.131	1.048	1.309	1.562
beta0_black[4]	2.368	0.191	1.880	2.397	2.674
beta0_black[5]	1.568	1.929	-2.724	1.644	5.607
beta0_black[6]	1.577	1.948	-2.897	1.638	5.667
beta0_black[7]	1.557	2.015	-2.955	1.617	5.902
beta0_black[8]	1.249	0.238	0.781	1.260	1.677
beta0_black[9]	2.392	0.281	1.804	2.408	2.892
beta0_black[10]	1.456	0.133	1.193	1.458	1.716
beta0_black[11]	3.397	0.210	2.918	3.415	3.739
beta0_black[12]	4.481	0.189	4.113	4.484	4.850
beta0_black[13]	-0.113	0.234	-0.580	-0.106	0.317
beta0_black[14]	2.160	0.470	0.776	2.250	2.794
beta0_black[15]	1.157	0.291	0.486	1.205	1.541
beta0_black[16]	4.024	0.633	1.981	4.210	4.546
beta2_black[1]	0.836	4.297	-8.246	1.300	9.055
beta2_black[2]	0.288	4.111	-8.214	0.307	7.888
beta2_black[3]	0.380	4.327	-8.487	0.571	8.522
beta2_black[4]	-0.042	4.253	-8.257	-0.113	7.912
beta2_black[5]	-0.373	4.316	-8.861	-0.449	8.160
beta2_black[6]	-0.484	4.296	-8.587	-0.616	8.426
beta2_black[7]	-0.379	4.361	-8.788	-0.503	8.569
beta2_black[8]	-0.678	4.410	-9.338	-0.839	8.356
beta2_black[9]	-0.524	4.296	-8.797	-0.799	8.334
beta2_black[10]	-0.644	4.300	-8.987	-0.851	8.361
beta2_black[11]	-1.697	2.029	-7.001	-1.237	0.887
beta2_black[12]	-2.424	1.810	-7.421	-1.877	-0.514
beta2_black[13]	-2.283	1.921	-7.607	-1.663	-0.449
beta2_black[14]	-1.781	1.990	-7.388	-1.086	-0.091
beta2_black[15]	-2.090	2.331	-7.752	-1.573	1.152
beta2_black[16]	-1.786	3.037	-9.013	-1.412	3.715
beta3_black[1]	33.682	8.480	18.640	35.556	44.107
beta3_black[2]	29.936	7.973	18.369	29.120	44.935
beta3_black[3]	29.950	7.848	18.590	29.217	44.935
beta3_black[4]	30.739	7.566	18.538	31.440	44.932
beta3_black[5]	29.753	7.891	18.451	28.939	44.947
beta3_black[6]	29.991	7.885	18.493	29.199	44.721
beta3_black[7]	29.812	7.915	18.421	28.628	44.612
beta3_black[8]	30.280	7.904	18.575	29.505	44.745
beta3_black[9]	30.322	8.121	18.503	29.493	44.992
beta3_black[10]	29.435	7.876	18.488	28.152	44.911
beta3_black[11]	30.163	6.812	18.710	30.017	43.686
beta3_black[12]	32.501	1.468	28.262	32.818	33.948
beta3_black[13]	39.302	0.717	37.700	39.370	40.530
beta3_black[14]	37.789	4.328	22.861	38.671	44.446
beta3_black[15]	31.822	7.894	18.597	31.616	45.140
beta3_black[16]	28.658	7.571	18.444	27.101	44.854
beta4_black[1]	-0.274	0.184	-0.636	-0.270	0.088
beta4_black[2]	0.243	0.174	-0.092	0.242	0.585
beta4_black[3]	-0.936	0.186	-1.300	-0.936	-0.578
beta4_black[4]	0.425	0.213	0.024	0.425	0.843
beta4_black[5]	0.238	2.627	-4.201	0.167	5.071
beta4_black[6]	0.132	2.861	-5.054	0.143	5.099
beta4_black[7]	0.134	3.456	-5.217	0.146	4.921
beta4_black[8]	-0.704	0.363	-1.417	-0.701	-0.016
beta4_black[9]	1.474	1.040	-0.106	1.371	3.944
beta4_black[10]	0.026	0.178	-0.324	0.029	0.386
beta4_black[11]	-0.690	0.199	-1.081	-0.690	-0.306
beta4_black[12]	0.289	0.323	-0.320	0.292	0.941
beta4_black[13]	-1.194	0.219	-1.624	-1.197	-0.768
beta4_black[14]	-0.128	0.228	-0.585	-0.130	0.322
beta4_black[15]	-0.889	0.208	-1.300	-0.886	-0.493
beta4_black[16]	-0.595	0.223	-1.027	-0.596	-0.143
mu_beta0_black[1]	1.319	0.878	-0.621	1.348	3.034
mu_beta0_black[2]	1.574	0.910	-0.663	1.638	3.337
mu_beta0_black[3]	2.296	0.962	0.250	2.343	4.124
tau_beta0_black[1]	0.764	0.738	0.059	0.539	2.680
tau_beta0_black[2]	2.261	5.027	0.058	0.921	12.510
tau_beta0_black[3]	0.254	0.167	0.052	0.216	0.692
beta0_dsr[11]	-3.044	0.290	-3.613	-3.042	-2.470
beta0_dsr[12]	4.481	0.273	3.968	4.475	5.016
beta0_dsr[13]	-1.554	0.282	-2.129	-1.543	-1.019
beta0_dsr[14]	-4.142	0.496	-5.133	-4.138	-3.173
beta0_dsr[15]	-2.396	0.269	-2.907	-2.401	-1.860
beta0_dsr[16]	-3.073	0.354	-3.754	-3.067	-2.395
beta1_dsr[11]	4.917	0.303	4.337	4.913	5.519
beta1_dsr[12]	6.347	4.244	2.358	5.209	18.557
beta1_dsr[13]	3.019	0.300	2.481	3.009	3.651
beta1_dsr[14]	6.772	0.525	5.758	6.762	7.835
beta1_dsr[15]	3.577	0.272	3.036	3.573	4.107
beta1_dsr[16]	5.859	0.374	5.134	5.853	6.611
beta2_dsr[11]	-8.130	2.267	-13.432	-7.740	-4.708
beta2_dsr[12]	-6.999	2.540	-12.647	-6.820	-2.424
beta2_dsr[13]	-6.301	2.672	-12.045	-6.228	-1.345
beta2_dsr[14]	-6.544	2.340	-11.757	-6.321	-2.713
beta2_dsr[15]	-7.529	2.312	-12.963	-7.200	-3.737
beta2_dsr[16]	-7.765	2.274	-13.091	-7.420	-4.292
beta3_dsr[11]	43.483	0.148	43.211	43.480	43.769
beta3_dsr[12]	33.996	0.652	32.359	34.135	34.795
beta3_dsr[13]	43.211	0.393	42.809	43.180	43.819
beta3_dsr[14]	43.267	0.146	43.079	43.232	43.644
beta3_dsr[15]	43.475	0.189	43.137	43.472	43.824
beta3_dsr[16]	43.441	0.152	43.177	43.430	43.747
beta4_dsr[11]	0.668	0.209	0.269	0.667	1.073
beta4_dsr[12]	0.318	0.462	-0.566	0.312	1.246
beta4_dsr[13]	-0.089	0.211	-0.516	-0.089	0.319
beta4_dsr[14]	0.208	0.253	-0.284	0.202	0.699
beta4_dsr[15]	0.989	0.213	0.567	0.990	1.403
beta4_dsr[16]	0.181	0.230	-0.266	0.183	0.633
beta0_slope[11]	-2.000	0.155	-2.300	-1.997	-1.695
beta0_slope[12]	-4.689	0.258	-5.191	-4.687	-4.191
beta0_slope[13]	-1.423	0.210	-1.904	-1.403	-1.073
beta0_slope[14]	-2.640	0.204	-3.036	-2.645	-2.245
beta0_slope[15]	-1.699	0.151	-2.004	-1.701	-1.402
beta0_slope[16]	-2.740	0.172	-3.076	-2.740	-2.396
beta1_slope[11]	4.378	0.295	3.816	4.378	4.959
beta1_slope[12]	4.874	0.537	3.819	4.869	5.932
beta1_slope[13]	2.688	0.522	1.992	2.605	4.260
beta1_slope[14]	6.015	0.806	4.669	5.925	7.913
beta1_slope[15]	2.032	0.277	1.496	2.034	2.577
beta1_slope[16]	5.289	0.389	4.543	5.282	6.075
beta2_slope[11]	7.715	2.302	4.027	7.387	12.953
beta2_slope[12]	6.388	2.616	1.874	6.135	12.074
beta2_slope[13]	4.366	2.825	0.336	3.990	10.679
beta2_slope[14]	2.701	2.494	0.741	1.505	9.370
beta2_slope[15]	6.505	2.571	2.554	6.155	12.378
beta2_slope[16]	7.115	2.358	3.398	6.865	12.513
beta3_slope[11]	43.489	0.153	43.213	43.487	43.787
beta3_slope[12]	43.412	0.225	43.046	43.389	43.852
beta3_slope[13]	43.579	0.509	42.647	43.605	44.430
beta3_slope[14]	44.676	0.425	43.792	44.733	45.324
beta3_slope[15]	43.598	0.247	43.123	43.610	44.030
beta3_slope[16]	43.469	0.169	43.180	43.457	43.800
beta4_slope[11]	-0.455	0.205	-0.857	-0.455	-0.059
beta4_slope[12]	-1.209	0.666	-2.744	-1.113	-0.181
beta4_slope[13]	0.172	0.208	-0.230	0.172	0.569
beta4_slope[14]	-0.117	0.246	-0.607	-0.115	0.371
beta4_slope[15]	-0.207	0.195	-0.589	-0.205	0.184
beta4_slope[16]	-0.157	0.230	-0.614	-0.159	0.292
sigma_H[1]	0.196	0.053	0.097	0.193	0.306
sigma_H[2]	0.171	0.030	0.118	0.168	0.237
sigma_H[3]	0.199	0.042	0.124	0.197	0.284
sigma_H[4]	0.420	0.078	0.290	0.411	0.593
sigma_H[5]	0.988	0.204	0.610	0.981	1.421
sigma_H[6]	0.372	0.205	0.028	0.362	0.803
sigma_H[7]	0.295	0.057	0.203	0.288	0.429
sigma_H[8]	0.427	0.092	0.285	0.419	0.624
sigma_H[9]	0.521	0.123	0.332	0.502	0.812
sigma_H[10]	0.218	0.043	0.144	0.215	0.316
sigma_H[11]	0.279	0.046	0.199	0.274	0.379
sigma_H[12]	0.449	0.166	0.214	0.428	0.775
sigma_H[13]	0.213	0.038	0.145	0.210	0.297
sigma_H[14]	0.509	0.096	0.341	0.502	0.717
sigma_H[15]	0.250	0.041	0.181	0.246	0.342
sigma_H[16]	0.229	0.044	0.156	0.225	0.326
lambda_H[1]	2.970	4.720	0.149	1.716	13.492
lambda_H[2]	8.021	7.210	0.790	6.097	26.992
lambda_H[3]	6.479	10.475	0.275	3.018	34.402
lambda_H[4]	0.006	0.004	0.001	0.005	0.017
lambda_H[5]	6.801	25.120	0.032	0.954	47.762
lambda_H[6]	7.864	15.845	0.008	1.082	47.353
lambda_H[7]	0.014	0.010	0.002	0.012	0.041
lambda_H[8]	7.888	10.335	0.004	4.220	36.673
lambda_H[9]	0.016	0.011	0.003	0.014	0.042
lambda_H[10]	0.310	0.552	0.032	0.196	1.187
lambda_H[11]	0.253	0.364	0.012	0.134	1.149
lambda_H[12]	5.127	6.709	0.189	2.896	21.785
lambda_H[13]	3.326	3.048	0.211	2.460	11.133
lambda_H[14]	3.694	4.681	0.249	2.231	16.111
lambda_H[15]	0.028	0.081	0.003	0.017	0.116
lambda_H[16]	1.678	2.351	0.079	0.976	6.855
mu_lambda_H[1]	4.319	1.927	1.208	4.146	8.500
mu_lambda_H[2]	3.870	1.967	0.595	3.719	8.051
mu_lambda_H[3]	3.646	1.867	0.786	3.389	7.838
sigma_lambda_H[1]	8.571	4.268	2.044	7.975	17.842
sigma_lambda_H[2]	8.500	4.714	1.032	7.947	18.641
sigma_lambda_H[3]	6.402	3.960	0.997	5.552	16.046
beta_H[1,1]	6.843	1.099	4.242	7.012	8.484
beta_H[2,1]	9.879	0.478	8.855	9.898	10.763
beta_H[3,1]	8.003	0.784	6.157	8.105	9.291
beta_H[4,1]	9.376	7.889	-6.900	9.536	24.009
beta_H[5,1]	0.171	2.384	-4.787	0.324	4.382
beta_H[6,1]	3.230	3.870	-6.608	4.707	7.552
beta_H[7,1]	1.245	5.602	-11.286	1.629	10.968
beta_H[8,1]	2.072	6.691	-2.473	1.242	22.607
beta_H[9,1]	12.933	5.627	1.820	12.961	24.392
beta_H[10,1]	7.057	1.683	3.533	7.090	10.387
beta_H[11,1]	5.303	3.426	-2.559	6.027	10.097
beta_H[12,1]	2.593	1.043	0.740	2.501	4.891
beta_H[13,1]	9.004	0.965	6.838	9.107	10.524
beta_H[14,1]	2.224	1.040	0.184	2.224	4.313
beta_H[15,1]	-5.996	3.970	-12.939	-6.366	2.870
beta_H[16,1]	3.003	2.132	-0.765	2.872	7.714
beta_H[1,2]	7.900	0.246	7.402	7.909	8.368
beta_H[2,2]	10.024	0.139	9.757	10.027	10.301
beta_H[3,2]	8.952	0.203	8.541	8.954	9.349
beta_H[4,2]	3.554	1.474	0.821	3.517	6.569
beta_H[5,2]	1.972	0.971	0.054	1.968	3.829
beta_H[6,2]	5.797	1.068	3.321	5.974	7.454
beta_H[7,2]	2.421	1.071	0.519	2.359	4.797
beta_H[8,2]	2.807	1.680	-2.771	3.109	4.239
beta_H[9,2]	3.437	1.089	1.423	3.411	5.703
beta_H[10,2]	8.180	0.349	7.459	8.186	8.845
beta_H[11,2]	9.709	0.613	8.819	9.593	11.139
beta_H[12,2]	3.939	0.372	3.237	3.931	4.692
beta_H[13,2]	9.118	0.257	8.659	9.103	9.651
beta_H[14,2]	4.011	0.346	3.334	3.994	4.706
beta_H[15,2]	11.351	0.716	9.770	11.409	12.641
beta_H[16,2]	4.664	0.783	3.110	4.654	6.206
beta_H[1,3]	8.500	0.244	8.056	8.491	8.993
beta_H[2,3]	10.076	0.117	9.838	10.073	10.318
beta_H[3,3]	9.618	0.166	9.301	9.617	9.968
beta_H[4,3]	-2.516	0.892	-4.217	-2.522	-0.755
beta_H[5,3]	3.863	0.629	2.557	3.868	5.068
beta_H[6,3]	8.095	1.203	6.440	7.719	10.745
beta_H[7,3]	-2.477	0.709	-3.904	-2.467	-1.075
beta_H[8,3]	5.344	0.757	4.648	5.199	8.039
beta_H[9,3]	-2.717	0.728	-4.185	-2.697	-1.262
beta_H[10,3]	8.751	0.277	8.224	8.745	9.317
beta_H[11,3]	8.548	0.283	7.950	8.566	9.059
beta_H[12,3]	5.249	0.318	4.489	5.290	5.757
beta_H[13,3]	8.815	0.179	8.436	8.822	9.152
beta_H[14,3]	5.677	0.267	5.097	5.695	6.138
beta_H[15,3]	10.350	0.329	9.726	10.347	11.010
beta_H[16,3]	6.681	0.492	5.568	6.735	7.495
beta_H[1,4]	8.267	0.174	7.889	8.280	8.575
beta_H[2,4]	10.134	0.121	9.875	10.141	10.347
beta_H[3,4]	10.110	0.165	9.749	10.129	10.396
beta_H[4,4]	11.787	0.445	10.877	11.798	12.624
beta_H[5,4]	5.523	0.770	4.278	5.429	7.319
beta_H[6,4]	7.183	0.869	5.135	7.435	8.362
beta_H[7,4]	8.196	0.336	7.533	8.197	8.846
beta_H[8,4]	6.669	0.340	5.688	6.706	7.138
beta_H[9,4]	7.179	0.465	6.270	7.174	8.108
beta_H[10,4]	7.760	0.243	7.295	7.751	8.281
beta_H[11,4]	9.292	0.204	8.906	9.290	9.687
beta_H[12,4]	7.125	0.215	6.725	7.116	7.580
beta_H[13,4]	9.004	0.147	8.699	9.004	9.288
beta_H[14,4]	7.657	0.215	7.232	7.657	8.081
beta_H[15,4]	9.447	0.237	8.962	9.448	9.916
beta_H[16,4]	9.160	0.200	8.795	9.145	9.581
beta_H[1,5]	8.972	0.145	8.670	8.975	9.243
beta_H[2,5]	10.782	0.092	10.608	10.783	10.964
beta_H[3,5]	10.920	0.172	10.609	10.916	11.264
beta_H[4,5]	8.369	0.457	7.460	8.359	9.277
beta_H[5,5]	5.384	0.605	3.927	5.443	6.409
beta_H[6,5]	8.751	0.603	7.860	8.624	10.284
beta_H[7,5]	6.814	0.316	6.193	6.805	7.443
beta_H[8,5]	8.230	0.270	7.847	8.199	9.005
beta_H[9,5]	8.225	0.476	7.270	8.220	9.153
beta_H[10,5]	10.080	0.233	9.614	10.080	10.541
beta_H[11,5]	11.541	0.235	11.062	11.541	11.998
beta_H[12,5]	8.464	0.195	8.085	8.464	8.857
beta_H[13,5]	10.011	0.132	9.760	10.008	10.278
beta_H[14,5]	9.179	0.235	8.746	9.167	9.655
beta_H[15,5]	11.171	0.252	10.665	11.169	11.674
beta_H[16,5]	9.959	0.156	9.642	9.963	10.252
beta_H[1,6]	10.185	0.195	9.852	10.168	10.613
beta_H[2,6]	11.512	0.107	11.303	11.512	11.729
beta_H[3,6]	10.814	0.164	10.466	10.826	11.101
beta_H[4,6]	12.901	0.820	11.265	12.917	14.526
beta_H[5,6]	5.904	0.614	4.753	5.876	7.185
beta_H[6,6]	8.804	0.636	7.026	8.907	9.730
beta_H[7,6]	9.805	0.535	8.735	9.813	10.864
beta_H[8,6]	9.484	0.372	8.503	9.532	9.975
beta_H[9,6]	8.437	0.789	6.934	8.420	10.043
beta_H[10,6]	9.520	0.317	8.841	9.549	10.076
beta_H[11,6]	10.804	0.360	10.027	10.828	11.443
beta_H[12,6]	9.369	0.258	8.869	9.362	9.896
beta_H[13,6]	11.059	0.163	10.763	11.052	11.407
beta_H[14,6]	9.873	0.290	9.311	9.877	10.431
beta_H[15,6]	10.865	0.438	9.973	10.862	11.721
beta_H[16,6]	10.572	0.207	10.114	10.585	10.946
beta_H[1,7]	10.838	0.866	8.806	10.963	12.237
beta_H[2,7]	12.204	0.427	11.297	12.217	13.021
beta_H[3,7]	10.524	0.699	8.936	10.597	11.664
beta_H[4,7]	2.382	4.237	-5.926	2.287	10.672
beta_H[5,7]	6.471	1.855	2.972	6.383	10.548
beta_H[6,7]	9.564	2.363	4.834	9.503	15.510
beta_H[7,7]	10.782	2.727	5.463	10.751	16.189
beta_H[8,7]	11.117	1.433	9.391	10.943	14.298
beta_H[9,7]	4.581	4.039	-3.647	4.643	12.262
beta_H[10,7]	9.808	1.435	7.140	9.735	12.888
beta_H[11,7]	10.993	1.748	7.803	10.872	14.738
beta_H[12,7]	10.037	0.947	7.959	10.118	11.556
beta_H[13,7]	11.668	0.740	9.824	11.771	12.846
beta_H[14,7]	10.463	0.953	8.353	10.529	12.129
beta_H[15,7]	12.158	2.296	7.707	12.169	16.912
beta_H[16,7]	11.972	1.051	10.320	11.816	14.439
beta0_H[1]	9.163	13.793	-19.625	9.040	39.079
beta0_H[2]	10.658	6.857	-2.644	10.602	24.680
beta0_H[3]	10.013	10.192	-11.150	10.187	30.885
beta0_H[4]	5.859	182.610	-372.280	4.739	376.981
beta0_H[5]	4.306	24.928	-42.080	4.340	54.725
beta0_H[6]	7.450	49.948	-102.731	7.733	113.599
beta0_H[7]	4.902	129.980	-252.724	6.254	262.530
beta0_H[8]	7.799	53.220	-21.047	6.391	41.894
beta0_H[9]	7.004	120.419	-231.664	8.191	250.886
beta0_H[10]	8.830	33.117	-61.117	9.143	77.964
beta0_H[11]	10.382	47.105	-89.162	10.067	109.059
beta0_H[12]	6.902	11.786	-14.053	6.625	30.177
beta0_H[13]	10.039	11.737	-12.173	10.044	33.241
beta0_H[14]	7.193	10.665	-13.933	7.139	28.924
beta0_H[15]	11.285	108.080	-208.452	11.925	232.792
beta0_H[16]	7.906	18.185	-30.598	8.305	44.804